Re: The simple essence of Proof Theoretic Semantics

On 7/3/2026 9:52 PM, olcott wrote:
> On 7/3/2026 5:51 PM, André G. Isaak wrote:
>> On 2026-07-03 16:37, olcott wrote:
>>> On 7/3/2026 1:47 PM, André G. Isaak wrote:
>>>> On 2026-07-03 12:36, olcott wrote:
>>>>> On 7/3/2026 1:18 PM, dbush wrote:
>>>>
>>>>>> If an algorithm takes an input and produces an output, that is by 
>>>>>> definition a mapping. 
>>>>> That only proves that the definition is incoherent.
>>>>> The coherent way that it actually works is that
>>>>> inputs are transformed into outputs by applying
>>>>> finite string transformation rules to inputs to
>>>>> derive outputs.
>>>>
>>>> Apparently you don't understand the difference between a mapping and 
>>>> an algorithm. They are two different things.
>>>>
>>>> André
>>>>
>>>
>>> A function that ignores its input and only returns 0
>>> is not any sort of halt function.
>>
>> He was defining 'mapping', not 'halt function'.
>>
>> André
>>
> 
> A actual halt function must compute 
The mathematical halting function:


Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
described as <X> with input Y:

A solution to the halting problem is an algorithm H that computes the 
following mapping:

(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly